Final answer:
The initial equation with cosine exceeding the range is incorrect. Correcting the range and using arccos to solve for the angle, we find all possible values of x considering the periodicity of the cosine function.
Step-by-step explanation:
The original equation presented by the student, cos(3x) = 11, contains an error since the cosine function can only have values between -1 and 1. However, moving forward with the concept of solving for angles using inverse trigonometric functions, we can consider a corrected equation such as cos(3x) = A, where A is within the correct range. We would then use the inverse cosine function (arccos) to find the angle, resulting in 3x = arccos(A). To find all values of x between 0 and 2π that satisfy this equation, we would first solve for 3x = arccos(A) and then divide the result by 3 to find x. Due to the periodic nature of the cosine function, additional solutions can be found by adding integer multiples of 2π to the obtained angles before dividing by 3.